library(tidyverse)
library(knitr)
library(plotly) ; library(viridis) ; library(gridExtra) ; library(RColorBrewer)
library(biomaRt)
library(Rtsne)
library(caret) ; library(ROCR) ; library(car)
library(corrplot)
library(expss) ; library(knitr)
SFARI_colour_hue = function(r) {
pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}
In 20_04_07_LR.html we performed a logistic regression but we discovered that the features were strongly correlated. This inflates the standard error of the coefficients, making them no longer interpretable.
# Clusterings
clustering_selected = 'DynamicHybridMergedSmall'
clusterings = read_csv('./../Data/clusters.csv')
clusterings$Module = clusterings[,clustering_selected] %>% data.frame %>% unlist %>% unname
assigned_module = data.frame('ID' = clusterings$ID, 'Module' = clusterings$Module)
# Original dataset
original_dataset = read.csv(paste0('./../Data/dataset_', clustering_selected, '.csv'), row.names=1)
# Model dataset
load('./../Data/LR_model.RData')
# Add gene symbol
getinfo = c('ensembl_gene_id','external_gene_id')
mart = useMart(biomart='ENSEMBL_MART_ENSEMBL', dataset='hsapiens_gene_ensembl',
host='feb2014.archive.ensembl.org')
gene_names = getBM(attributes=getinfo, filters=c('ensembl_gene_id'), values=rownames(dataset), mart=mart)
Variance Inflation Factor (VIF) and correlation plot
# VIF
plot_data = data.frame('Feature' = car::vif(fit) %>% sort %>% names,
'VIF' = car::vif(fit) %>% sort %>% unname) %>%
mutate(outlier = VIF>10)
plot_data %>% ggplot(aes(reorder(Feature, -VIF), VIF, fill = !outlier)) + geom_bar(stat='identity') + scale_y_log10() +
geom_hline(yintercept = 10, color = 'gray', linetype = 'dashed') + xlab('Model Features') + theme_minimal() +
theme(legend.position = 'none', axis.text.x = element_text(angle = 90, hjust = 1))
# Correlation plot
corrplot.mixed(cor(train_set[,-ncol(train_set)]), lower = 'number', lower.col = 'gray', number.cex = .6, tl.pos = 'l', tl.col = '#666666')
rm(getinfo, mart, clusterings)
Remove all variables with a VIF>10: We would lose all but three of our variables, not ideal
Do Principal Component Regression: We would lose the relation between the prediction and the original features, which would be interesting to study
Don’t do anything: Multicollinearity affects the coefficients and p-values of the regression, but it doesn’t affect the predictions, precision of the predictions or the goodness-of-fit statistics ref, but as with the previous option, we cannot study the coefficients of the regression
Use Ridge Regression
Using the same train and test sets created in 20_04_07_LR.html
Train model
train_set$SFARI = train_set$SFARI %>% as.factor
lambda_seq = 10^seq(1, -4, by = -.1)
set.seed(123)
fit = train(SFARI ~., data = train_set, method = 'glmnet', trControl = trainControl('cv', number = 10),
tuneGrid = expand.grid(alpha = 0, lambda = lambda_seq))
cat(paste0('The best model has a lambda of ', round(fit$bestTune$lambda,4)))
## The best model has a lambda of 0.0631
rm(lambda_seq)
Predict labels in test set
predictions = fit %>% predict(test_set, type='prob')
test_set$prob = predictions$`TRUE`
test_set$pred = test_set$prob>0.5
rm(predictions)
conf_mat = test_set %>% apply_labels(SFARI = 'Actual Labels',
prob = 'Assigned Probability',
pred = 'Label Prediction')
cro(conf_mat$SFARI, list(conf_mat$pred, total()))
|  Label Prediction |  #Total | |||
|---|---|---|---|---|
| Â FALSEÂ | Â TRUEÂ | Â | ||
|  Actual Labels | ||||
| Â Â Â FALSEÂ | 8031 | 4226 | Â | 12257 |
| Â Â Â TRUEÂ | 81 | 96 | Â | 177 |
|    #Total cases | 8112 | 4322 |  | 12434 |
rm(conf_mat)
acc = mean(test_set$SFARI==test_set$pred)
cat(paste0('Accuracy = ', round(acc,4)))
## Accuracy = 0.6536
rm(acc)
pred_ROCR = prediction(test_set$prob, test_set$SFARI)
roc_ROCR = performance(pred_ROCR, measure='tpr', x.measure='fpr')
AUC = performance(pred_ROCR, measure='auc')@y.values[[1]]
plot(roc_ROCR, main=paste0('ROC curve (AUC=',round(AUC,2),')'), col='#009999')
abline(a=0, b=1, col='#666666')
lift_ROCR = performance(pred_ROCR, measure='lift', x.measure='rpp')
plot(lift_ROCR, main='Lift curve', col='#86b300')
rm(pred_ROCR, roc_ROCR, AUC, lift_ROCR)
gene_corr_info = dataset %>% mutate('ID' = rownames(dataset)) %>% dplyr::select(ID, MTcor, SFARI) %>% left_join(assigned_module, by ='ID') %>%
mutate(Module = gsub('#','',Module))
coef_info = coef(fit$finalModel, fit$bestTune$lambda) %>% as.matrix %>% data.frame %>% dplyr::rename('coef' = X1) %>%
mutate('feature' = gsub('MM.','',rownames(.))) %>% left_join(gene_corr_info, by = c('feature' = 'Module')) %>%
dplyr::select(feature, coef, MTcor, SFARI) %>% group_by(feature, coef, MTcor) %>% summarise('SFARI_perc' = mean(SFARI)) %>%
arrange(desc(coef))
kable(coef_info %>% dplyr::select(feature, coef) %>% rename('Feature' = feature, 'Coefficient' = coef),
align = 'cc', caption = 'Regression Coefficients')
| Feature | Coefficient |
|---|---|
| FF62BC | 0.8589655 |
| 00A7FF | 0.6848483 |
| FE6E8A | 0.5886960 |
| 00BA38 | 0.5350276 |
| 00BF7D | 0.4516837 |
| D89000 | 0.3579370 |
| 00BCD8 | 0.3572140 |
| 00C0AF | 0.3081397 |
| D376FF | 0.2547095 |
| F8766D | 0.2214329 |
| 39B600 | 0.2082034 |
| B79F00 | 0.1676503 |
| F564E3 | 0.1395635 |
| 00C097 | 0.1129423 |
| 00BFC4 | 0.1073604 |
| FF67A4 | 0.0935501 |
| E58700 | 0.0914464 |
| 6BB100 | 0.0578363 |
| MTcor | 0.0222060 |
| absGS | -0.0331095 |
| B983FF | -0.0342090 |
| 00BD5F | -0.0408827 |
| A3A500 | -0.0630330 |
| EF7F49 | -0.0715613 |
| GS | -0.0996442 |
| 00B0F6 | -0.1285335 |
| E76BF3 | -0.1397291 |
| FD61D1 | -0.1460062 |
| 8AAB00 | -0.1559012 |
| (Intercept) | -0.1945565 |
| C99800 | -0.2764409 |
| 9590FF | -0.3914160 |
| 00B7E9 | -0.3946339 |
| 619CFF | -0.4782678 |
ggplotly(coef_info %>% dplyr::rename('Module' = feature) %>% filter(!is.na(MTcor)) %>%
ggplot(aes(coef, SFARI_perc)) + geom_smooth(method = 'lm', color = 'gray', alpha = 0.1) +
geom_point(aes(id = Module), color = paste0('#',coef_info$feature[!is.na(coef_info$MTcor)])) +
theme_minimal() + xlab('Coefficient') +
ylab('% of SFARI genes in Module'))
This is not a surprise since we knew that there was a negative relation between SFARI genes and Module-Diagnosis correlation from Preprocessing/Gandal/AllRegions/RMarkdowns/20_04_03_WGCNA_modules_EA.html. The fact that the relation between coefficient and Module-Diagnosis correlation is so small now could even be a good sign that the model is picking some biological signal as well as the SFARI patterns (since the relation with the biological signals is positive)
ggplotly(coef_info %>% dplyr::rename('Module' = feature) %>% filter(!is.na(MTcor)) %>%
ggplot(aes(coef, MTcor)) + geom_smooth(method = 'lm', color = 'gray', alpha = 0.1) +
geom_point(aes(id = Module), color = paste0('#',coef_info$feature[!is.na(coef_info$MTcor)])) +
theme_minimal() + xlab('Coefficient') +
ylab('Module-Diagnosis correlation'))
SFARI genes have a slightly higher score distribution than the rest
plot_data = test_set %>% dplyr::select(prob, SFARI)
ggplotly(plot_data %>% ggplot(aes(prob, fill=SFARI, color=SFARI)) + geom_density(alpha=0.3) + xlab('Score') +
geom_vline(xintercept = mean(plot_data$prob[plot_data$SFARI]), color = '#00C0C2', linetype = 'dashed') +
geom_vline(xintercept = mean(plot_data$prob[!plot_data$SFARI]), color = '#FF7371', linetype = 'dashed') +
theme_minimal() + ggtitle('Model score distribution by SFARI Label'))
There seems to be a positive relation between the SFARI scores and the probability assigned by the model
The number of observations when separating the test set by SFARI score is quite small, so this is not a robust result, specially for scores 1, 2 and 6
plot_data = test_set %>% mutate(ID=rownames(test_set)) %>% dplyr::select(ID, prob) %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID') %>%
dplyr::select(ID, prob, gene.score) %>% apply_labels(gene.score='SFARI Gene score')
cro(plot_data$gene.score)
|  #Total | |
|---|---|
|  SFARI Gene score | |
| Â Â Â 1Â | 5 |
| Â Â Â 2Â | 12 |
| Â Â Â 3Â | 38 |
| Â Â Â 4Â | 86 |
| Â Â Â 5Â | 32 |
| Â Â Â 6Â | 4 |
|    None | 12257 |
|    #Total cases | 12434 |
mean_vals = plot_data %>% group_by(gene.score) %>% summarise(mean_prob = mean(prob))
ggplotly(plot_data %>% ggplot(aes(gene.score, prob, fill=gene.score)) + geom_boxplot() +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
ggtitle('Distribution of probabilities by SFARI score') +
xlab('SFARI score') + ylab('Probability') + theme_minimal())
rm(mean_vals)
Genes with highest scores in test set
Considering the class imbalance in the test set (1:69), there are many SFARI scores in here (1:13)
3 of the 5 SFARI genes with a score of 1 in the test set are in this top 50 list
There aren’t any SFARI genes with a score lower than 3 (even though 69% of the SFARI genes in the test score have a score lower than 3)
test_set %>% dplyr::select(prob, SFARI) %>% mutate(ID = rownames(test_set)) %>%
arrange(desc(prob)) %>% top_n(50, wt=prob) %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID') %>%
left_join(gene_names, by = c('ID'='ensembl_gene_id')) %>%
dplyr::rename('GeneSymbol' = external_gene_id, 'Probability' = prob, 'ModuleDiagnosis_corr' = MTcor, 'GeneSignificance' = GS) %>%
mutate(ModuleDiagnosis_corr = round(ModuleDiagnosis_corr,4), Probability = round(Probability,4),
GeneSignificance = round(GeneSignificance,4)) %>%
dplyr::select(GeneSymbol, GeneSignificance, ModuleDiagnosis_corr, Module, Probability, gene.score) %>%
kable(caption = 'Genes with highest model probabilities from the test set')
| GeneSymbol | GeneSignificance | ModuleDiagnosis_corr | Module | Probability | gene.score |
|---|---|---|---|---|---|
| RPRD2 | -0.0922 | -0.6031 | #00BA38 | 0.8552 | None |
| MYCBP2 | -0.3975 | -0.6031 | #00BA38 | 0.8404 | None |
| GATAD2B | -0.4221 | -0.6031 | #00BA38 | 0.8316 | None |
| RNF111 | -0.2410 | 0.0586 | #FE6E8A | 0.8279 | None |
| KMT2D | -0.3255 | -0.6031 | #00BA38 | 0.8273 | None |
| ARID1B | 0.2711 | 0.1127 | #FF62BC | 0.8247 | 1 |
| EP400 | -0.1671 | -0.6031 | #00BA38 | 0.8212 | 3 |
| DROSHA | -0.4111 | -0.6031 | #00BA38 | 0.8183 | None |
| HUWE1 | -0.5026 | -0.6031 | #00BA38 | 0.8183 | None |
| ATN1 | -0.2052 | -0.6031 | #00BA38 | 0.8167 | None |
| RFX7 | 0.1372 | 0.0586 | #FE6E8A | 0.8150 | None |
| SMG7 | -0.2560 | -0.6031 | #00BA38 | 0.8148 | None |
| RASGRF1 | -0.7425 | -0.9514 | #00C0AF | 0.8139 | None |
| CLIP3 | -0.5368 | -0.6031 | #00BA38 | 0.8135 | None |
| KMT2A | 0.1347 | 0.7916 | #00C097 | 0.8127 | 1 |
| SAP130 | -0.2482 | -0.6031 | #00BA38 | 0.8110 | None |
| ASAP1 | -0.0896 | -0.6031 | #00BA38 | 0.8085 | None |
| TLN2 | -0.4783 | -0.9514 | #00C0AF | 0.8083 | None |
| UBR4 | -0.2856 | -0.6031 | #00BA38 | 0.8080 | None |
| FMNL1 | -0.2223 | -0.6031 | #00BA38 | 0.8073 | None |
| NFIC | -0.4414 | -0.6031 | #00BA38 | 0.8059 | None |
| AAK1 | -0.6913 | -0.9514 | #00C0AF | 0.8030 | None |
| NF1 | -0.4123 | -0.6031 | #00BA38 | 0.8025 | None |
| MIDN | -0.0520 | -0.6031 | #00BA38 | 0.8022 | None |
| CACNG3 | -0.4689 | -0.6031 | #00BA38 | 0.8022 | None |
| EIF4G3 | -0.4827 | -0.8040 | #00B7E9 | 0.8021 | None |
| UBAP2L | -0.3318 | -0.6031 | #00BA38 | 0.7994 | None |
| R3HDM2 | -0.4078 | -0.6031 | #00BA38 | 0.7989 | None |
| HUNK | -0.3273 | -0.6750 | #D376FF | 0.7986 | None |
| NAV1 | -0.1734 | -0.6031 | #00BA38 | 0.7961 | None |
| MAP3K13 | -0.4321 | -0.6750 | #D376FF | 0.7954 | None |
| MEF2D | -0.4172 | -0.6031 | #00BA38 | 0.7946 | None |
| SPTAN1 | -0.2903 | -0.6031 | #00BA38 | 0.7945 | None |
| POM121C | -0.2791 | -0.6031 | #00BA38 | 0.7942 | None |
| USP32 | -0.6248 | -0.6031 | #00BA38 | 0.7935 | None |
| KCNJ6 | -0.1379 | -0.9514 | #00C0AF | 0.7932 | None |
| BCL9 | 0.1299 | -0.6031 | #00BA38 | 0.7930 | None |
| CELF2 | -0.0605 | -0.9514 | #00C0AF | 0.7913 | None |
| AMPD3 | -0.2810 | -0.9514 | #00C0AF | 0.7912 | None |
| SCAF4 | 0.0185 | -0.6031 | #00BA38 | 0.7912 | None |
| FMN2 | -0.4335 | -0.6031 | #00BA38 | 0.7910 | None |
| NMNAT2 | -0.6817 | -0.9514 | #00C0AF | 0.7898 | None |
| BRPF3 | -0.4391 | -0.6031 | #00BA38 | 0.7895 | None |
| SIK3 | -0.1206 | -0.0094 | #00A7FF | 0.7891 | None |
| RAB7A | -0.4020 | -0.6031 | #00BA38 | 0.7890 | None |
| SGIP1 | -0.5363 | -0.6031 | #00BA38 | 0.7877 | None |
| FOXJ2 | 0.2507 | 0.1127 | #FF62BC | 0.7877 | None |
| RABGAP1L | -0.5226 | -0.6031 | #00BA38 | 0.7860 | None |
| KMT2E | 0.0723 | 0.7916 | #00C097 | 0.7858 | 3 |
| PRPF8 | -0.5452 | -0.6031 | #00BA38 | 0.7854 | None |
Selecting the Negative samples in the test set
negative_set = test_set %>% filter(SFARI)
negative_set = dataset %>% filter(!SFARI & !rownames(.) %in% rownames(train_set)) %>% dplyr::select(-SFARI)
rownames(negative_set) = rownames(dataset)[!dataset$SFARI & !rownames(dataset) %in% rownames(train_set)]
predictions = predict(fit, negative_set, type='prob') %>% as.vector
negative_set$prob = predictions$`TRUE`
negative_set$pred = negative_set$prob>0.5
negative_set_table = negative_set %>% apply_labels(prob = 'Assigned Probability',
pred = 'Label Prediction')
rm(predictions)
cro(negative_set_table$pred)
|  #Total | |
|---|---|
|  Label Prediction | |
| Â Â Â FALSEÂ | 8031 |
| Â Â Â TRUEÂ | 4226 |
|    #Total cases | 12257 |
cat(paste0('\n', sum(negative_set$pred), ' genes are predicted as ASD-related'))
##
## 4226 genes are predicted as ASD-related
negative_set %>% ggplot(aes(prob)) + geom_density(color='#F8766D', fill='#F8766D', alpha=0.5) +
geom_vline(xintercept=0.5, color='#333333', linetype='dotted') +
ggtitle('Probability distribution of the Negative samples in the test set') +
theme_minimal()
There’s a lot of noise, but the probability the model assigns to each gene seems to have a negative relation with the Gene Significance (under-expressed genes having on average the higher probabilities and over-expressed genes the lowest)
The pattern is strongest in under-expressed genes
negative_set %>% ggplot(aes(prob, GS, color=MTcor)) + geom_point() + geom_smooth(method='loess', color='#666666') +
geom_hline(yintercept=0, color='gray', linetype='dashed') + xlab('Probability') +
scale_color_gradientn(colours=c('#F8766D','white','#00BFC4')) +
ggtitle('Relation between Probability and Gene Significance') + theme_minimal()
On average, the model seems to be assigning a probability inversely proportional to the Module-Diagnosis correlation of the module, with the highest positively correlated modules having the lowest average probability and the highest negatively correlated modules the highest average probability. But the difference isn’t big
negative_set %>% ggplot(aes(MTcor, prob, color=GS)) + geom_point() + geom_smooth(method='loess', color='#666666') +
geom_hline(yintercept=mean(negative_set$prob), color='gray', linetype='dashed') +
scale_color_gradientn(colours=c('#F8766D','#F8766D','white','#00BFC4','#00BFC4')) +
xlab('Modules ordered by their correlation to ASD') + ylab('Model probability') +
theme_minimal()
Summarised version, plotting by module instead of by gene
The difference in the trend lines between this plot and the one above is that the one above takes all the points into consideration while this considers each module as an observation by itself, so the top one is strongly affected by big modules and the bottom one treats all modules the same
The model seems to give higher probabilities to genes belonging to modules with a small (absolute) correlation to Diagnosis (this is unexpected)
plot_data = negative_set %>% group_by(MTcor) %>% summarise(mean = mean(prob), sd = sd(prob), n = n()) %>%
mutate(MTcor_sign = ifelse(MTcor>0, 'Positive', 'Negative')) %>% left_join(original_dataset, by='MTcor') %>%
dplyr::select(Module, MTcor, MTcor_sign, mean, sd, n) %>% distinct()
colnames(plot_data)[1] = 'ID'
ggplotly(plot_data %>% ggplot(aes(MTcor, mean, size=n, color=MTcor_sign)) + geom_point(aes(id=ID)) +
geom_smooth(method='loess', color='gray', se=FALSE) + geom_smooth(method='lm', se=FALSE) +
xlab('Module-Diagnosis correlation') + ylab('Mean Probability by Model') + theme_minimal())
There is a positive relation between level of expression and probability, the model seems to be capturing indirectly the level of expression of the genes to make the prediction, so it’s introducing the same bias
# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.frame
mean_and_sd = data.frame(ID=rownames(datExpr), meanExpr=rowMeans(datExpr), sdExpr=apply(datExpr,1,sd))
plot_data = negative_set %>% mutate(ID=rownames(negative_set)) %>% left_join(mean_and_sd, by='ID') %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)) %>%
dplyr::select(ID, Module), by='ID')
colnames(plot_data)[ncol(plot_data)] = 'Module'
plot_data %>% ggplot(aes(meanExpr, prob)) + geom_point(alpha=0.2, color='#0099cc') +
geom_smooth(method='loess', color='gray', alpha=0.3) +
geom_smooth(method='lm', color='#999999', se=FALSE, alpha=1) +
theme_minimal() + ggtitle('Mean expression vs model probability by gene')
rm(mean_and_sd)
plot_data2 = plot_data %>% group_by(Module) %>% summarise(meanExpr = mean(meanExpr), meanProb = mean(prob), n=n())
ggplotly(plot_data2 %>% ggplot(aes(meanExpr, meanProb, size=n)) + geom_point(color=plot_data2$Module) +
geom_smooth(method='loess', se=TRUE, color='gray', alpha=0.1, size=0.7) +
geom_smooth(method='lm', se=FALSE, color='gray') + theme_minimal() + theme(legend.position='none') +
ggtitle('Mean expression vs model probability by Module'))
rm(plot_data2)
There is a relation between probability and lfc, so it **IS*() capturing a bit of true information (because lfc and mean expression were negatively correlated and it still has a positive relation in the model)
plot_data = negative_set %>% mutate(ID=rownames(negative_set)) %>%
left_join(DE_info %>% mutate(ID=rownames(DE_info)), by='ID')
plot_data %>% ggplot(aes(log2FoldChange, prob)) + geom_point(alpha=0.1, color='#0099cc') +
geom_smooth(method='loess', color='gray', alpha=0.3) +
theme_minimal() + ggtitle('lfc vs model probability by gene')
plot_data %>% mutate(DE = padj<0.05) %>% ggplot(aes(log2FoldChange, prob, color=DE)) + geom_point(alpha=0.1) +
geom_smooth(method='loess', alpha=0.3) +
theme_minimal() + ggtitle('lfc vs model probability by gene')
The model is capturing the mean level of expression of the genes (indirectly through module memberhsip), which is a strong bias found in the SFARI scores, but it seems to be capturing a bit of true biological signal as well (based on the GS and the log fold change plots)
save(train_set, test_set, negative_set, fit, dataset, file='./../Data/Ridge_model.RData')
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
##
## locale:
## [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB.UTF-8 LC_COLLATE=en_GB.UTF-8
## [5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
## [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] expss_0.10.2 corrplot_0.84 car_3.0-7 carData_3.0-3
## [5] ROCR_1.0-7 gplots_3.0.3 caret_6.0-86 lattice_0.20-40
## [9] Rtsne_0.15 biomaRt_2.40.5 RColorBrewer_1.1-2 gridExtra_2.3
## [13] viridis_0.5.1 viridisLite_0.3.0 plotly_4.9.2 knitr_1.28
## [17] forcats_0.5.0 stringr_1.4.0 dplyr_0.8.5 purrr_0.3.3
## [21] readr_1.3.1 tidyr_1.0.2 tibble_3.0.0 ggplot2_3.3.0
## [25] tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.1 backports_1.1.5
## [3] Hmisc_4.4-0 plyr_1.8.6
## [5] lazyeval_0.2.2 splines_3.6.3
## [7] BiocParallel_1.18.1 crosstalk_1.1.0.1
## [9] GenomeInfoDb_1.20.0 digest_0.6.25
## [11] foreach_1.5.0 htmltools_0.4.0
## [13] gdata_2.18.0 fansi_0.4.1
## [15] magrittr_1.5 checkmate_2.0.0
## [17] memoise_1.1.0 cluster_2.1.0
## [19] openxlsx_4.1.4 annotate_1.62.0
## [21] recipes_0.1.10 modelr_0.1.6
## [23] gower_0.2.1 matrixStats_0.56.0
## [25] prettyunits_1.1.1 jpeg_0.1-8.1
## [27] colorspace_1.4-1 blob_1.2.1
## [29] rvest_0.3.5 haven_2.2.0
## [31] xfun_0.12 crayon_1.3.4
## [33] RCurl_1.98-1.1 jsonlite_1.6.1
## [35] genefilter_1.66.0 survival_3.1-11
## [37] iterators_1.0.12 glue_1.3.2
## [39] gtable_0.3.0 zlibbioc_1.30.0
## [41] ipred_0.9-9 XVector_0.24.0
## [43] DelayedArray_0.10.0 shape_1.4.4
## [45] BiocGenerics_0.30.0 abind_1.4-5
## [47] scales_1.1.0 DBI_1.1.0
## [49] Rcpp_1.0.4 xtable_1.8-4
## [51] progress_1.2.2 htmlTable_1.13.3
## [53] foreign_0.8-75 bit_1.1-15.2
## [55] Formula_1.2-3 stats4_3.6.3
## [57] lava_1.6.7 prodlim_2019.11.13
## [59] glmnet_3.0-2 htmlwidgets_1.5.1
## [61] httr_1.4.1 acepack_1.4.1
## [63] ellipsis_0.3.0 pkgconfig_2.0.3
## [65] XML_3.99-0.3 farver_2.0.3
## [67] nnet_7.3-13 dbplyr_1.4.2
## [69] locfit_1.5-9.4 tidyselect_1.0.0
## [71] labeling_0.3 rlang_0.4.5
## [73] reshape2_1.4.3 AnnotationDbi_1.46.1
## [75] munsell_0.5.0 cellranger_1.1.0
## [77] tools_3.6.3 cli_2.0.2
## [79] generics_0.0.2 RSQLite_2.2.0
## [81] broom_0.5.5 evaluate_0.14
## [83] yaml_2.2.1 ModelMetrics_1.2.2.2
## [85] bit64_0.9-7 fs_1.4.0
## [87] zip_2.0.4 caTools_1.18.0
## [89] nlme_3.1-144 xml2_1.2.5
## [91] compiler_3.6.3 rstudioapi_0.11
## [93] png_0.1-7 curl_4.3
## [95] e1071_1.7-3 reprex_0.3.0
## [97] geneplotter_1.62.0 stringi_1.4.6
## [99] highr_0.8 Matrix_1.2-18
## [101] vctrs_0.2.4 pillar_1.4.3
## [103] lifecycle_0.2.0 data.table_1.12.8
## [105] bitops_1.0-6 GenomicRanges_1.36.1
## [107] latticeExtra_0.6-29 R6_2.4.1
## [109] KernSmooth_2.23-16 rio_0.5.16
## [111] IRanges_2.18.3 codetools_0.2-16
## [113] MASS_7.3-51.5 gtools_3.8.2
## [115] assertthat_0.2.1 SummarizedExperiment_1.14.1
## [117] DESeq2_1.24.0 withr_2.1.2
## [119] S4Vectors_0.22.1 GenomeInfoDbData_1.2.1
## [121] mgcv_1.8-31 parallel_3.6.3
## [123] hms_0.5.3 grid_3.6.3
## [125] rpart_4.1-15 timeDate_3043.102
## [127] class_7.3-16 rmarkdown_2.1
## [129] pROC_1.16.2 base64enc_0.1-3
## [131] Biobase_2.44.0 lubridate_1.7.4